Game of nim

ABSTRACT

I disclose a version of the game of Nim wherein one player plays against the machine. A number of marbles are positioned on an inclined rack. The player, by moving a slide adjacent to the lower end of the rack, and alternately the machine, by a motor driven arm, remove marbles. A removable game wheel is provided, depending upon the version of Nim being played. By the interaction of teeth and control pins underneath the game wheel and ratchets controlled by the slide and the machine motor, the game wheel rotates so as to remain in synchronism with the number of marbles on the rack and also, by a control arrangement controlled by the control pins, so as to terminate the machine&#39;&#39;s turn at positions most likely to allow the machine to win.

United States Patent [721 Inventor Robert L. Brass 1 Fellow St., Westport, Conn. 06880 [21] Appl No. 760,182 [22] Filed Sept. 17,1968 [45] Patented June 29, 1971 [54] GAME 01' MM 18 Claims, 7 Drawing Figs.

[52] US. Cl... 273/1(E) [51] 1nt.Cl. A631 9/00 [50] Field olSearch 273/130, 130A,l30AB,1R,1E;221/207 [56] References Cited UNITED STATES PATENTS 2,127,261 8/1938 Kramer et al. 273/1 (E) 2,930,616 3/1960 Holloway et a]. 273/43 A 3,501,644 3/1970 273/54 E 1,421,656 7/1922 273/130 2,215,544 9/1940 Condon-et a1. 273/130 (AB) Primary Examiner-Anton O. Oechsle Atlorney-James Warren Falk ABSTRACT: l disclose a version of the game of Nim wherein one player plays against the machine. A number of marbles are positioned on an inclined rack. The player, by moving a slide adjacent to the lower end of the rack, and alternately the machine, by a motor driven arm, remove marbles. A removable game wheel is provided, depending upon the version of Nim being played. By the interaction of teeth and control pins underneath the game wheel and ratchets controlled by the slide and the machine motor, the game wheel rotates so as to remain in synchronism with the number of marbles on the rack and also, by a control arrangement controlled by the control pins, so as to terminate the machines turn at positions most likely to allow the machine to win.

PATENTED JUN29|97I 3.589.722

sum 1 or 3 FIG.

INVENTOR ROBERT L. BRASS A 7'7'ORNE Y PATENTEUJUNZSISYII 3.589.722

SHEET 2 OF 3 FIG. 2

FIG. 3

lNl E N 70/? ROBERT LBRASS BY EM A TTORNE Y PATENTED JUN29l97l 3,589,722

ROBERT L. BRA S5 ATTORNEY GAME OF NIM BACKGROUND OF THE INVENTION (Simon & Schuster, 1959).

ln probably its oldest versions two players compete by picking up articles, such as matches or marbles, from a group of piles. The winner may be the one who either does or does not pick up the last article. Various limitations may be placed on the number of articles to be picked up at one time. Thus up to three, up to four, etc., may be picked at one time. Often this is done by placing the articles in a certain number of piles or rows and saying that one article is to be picked from as many piles as desired. Alternatively, the articles may be considered as a single group and then the players told to take up to a certain number of articles from this single group.

Because the various games of Nim can be analyzed with respect to their essential logic, machines can be devised which will play Nim with a single human opponent. A famous electrical version of a machine to play the game of Nim was exhibited at the New York Worlds Fair, l939-40, and is described in E. U. Condon et al. US. Pat. No. 2,215,544, Sept. 24, 1940. Other electrical and electronic machines may be built using logic elements as building blocks; such logic elements are now well known in the semiconductive logic and computer fields.

When one considers a machine to play the game of Nim as a small toy for home use it is readily-apparent that these prior machines are prohibitively complex and expensive, requiring, as they do, complex electronic circuitry.

Accordingly, it is an object of my invention to provide an inexpensive toy that will play the game of Nim with a single player.

It is a further object of my invention that a toy for playing the game of Nim should be capable of various versions, following different rules.

Another object of my invention is the attainment of a Nim playing machine without electrical or electronic logic elements.

SUMMARY OF THE INVENTION These and other objects of my invention are attained in one illustrative embodiment wherein a mechanical element, namely, a game wheel, provides the essential logic for the game. The game wheel is set in position in this embodiment so as to represent the number of articles, such as marbles, remaining in the game. The wheel is then rotated both as the player removes articles and as the machine itself removes articles. This rotation assures that the game wheel always indicatesthe number of articles remaining.

In accordance with an aspect of my invention the game wheel includes both a number of ratchet teeth arranged on its under side and also control pins selectively adjacent certain of the teeth. The game is arranged so that the player, in removing an article, causes a pawl mechanism to engage a single tooth and rotate the game wheel one position. Similarly, the game is arranged so that the mechanism for automatically removing an article, as part of the machine's tum, also causes a pawl mechanism to engage a tooth and rotate the wheel. However, when the wheel is rotated to a position giving the machine the winning or potential winning strategy or total of the remaining articles, then a control element is intercepted by one of the control pins and the machine ceases removing articles from the game.

In this specific embodiment the machine's turn is initiated by depression of a lever, thereby closing an electrical contact and also positioning the control bar in a notched post; the notched post prevents a spring from returning the lever to its normal position and releasing the electrical contacts. When the end of the control bar is contacted by one of the control pins, however, the bar is dislodged from the notch in the post and, because of the spring bias, returns the lever to its normal position.

Advantagcously, the articles in this embodiment are marbles which are removed from an inclined rack by the player who pulls back a slide at the end ofthe rack, allowing a single marble to roll off. The slide, in returning to its normal position under spring bias, causes a hooked pawl element to engage a ratchet tooth on the game wheel and rotate the wheel. Further, in this embodiment, the contacts closed by depression of the machines turn lever, energize an electrical motor which, through appropriate gearing, drives a crank member having attached to it two elements. The first of these is a reciprocating arm to the end of which is attached a small hand. The arm and hand are so positioned, with respect to the inclined rack, that the hand in moving to and fro removes a single marble from the end of the rack. The second element is another pawl mechanism including a hook element at its end for engaging a single game wheel ratchet'tooth.

The motor continues to cause. the dual action of the reciprocatingarm and hand and of the pawl mechanism until the contacts are opened, as discussedabove, thereby interrupting the electrical circuit.

In accordance with an aspect of my invention the game wheel which, by the positioning the control pins, provides the logic for the machines actions in accordancewith the particular game being played, is readily removable and may be replaced by a differentgame wheel whose control pins are selectively placed in other positions. Accordingly, a wide variety of games may be played with the one machine by merely replacing the game wheel. The alternate game wheels may be stored on the game itself or in a separate container.

It is a feature of myinvention that a game of Nim'include both player controlled and machine controlled elements for removing articles, with mechanical means controlling the removal of articles by the machine dependent upon the number of such articles remaining and the particular rule of the game being played.

it is another feature of my invention that this control be exercised by a game wheel having a plurality of pins selectively placed, the wheel being rotated as articles are removed and the pins engaging a control element which interrupts the action of the machine. I

it is further feature of myinvention that the wheel include ratchet teeth, one for each article, with pawl mechanisms engaging a single tooth at atime for rotation of the wheel just one position on removal of an article by either the machine of the player.

It is still another feature of my invention that the articles be marbles positioned on an inclined rack, the machine mechanism for removing the articles including an electrical motor and crank member for driving a reciprocating arm so positioned as to remove a single marble on each return movement.

It is still a further feature of my invention that the game wheel be readily removable so that it can be replaced by a different game wheel having the same teeth for rotation of the wheel in synchronism with the removal of marbles but with the control pins differently located so that a different game of Nim may be played with different rules as to the number of marbles that may be removed in a single move or as to whether the taker of the last marble is the winner or loser of the game.

DESCRIPTION OF THE DRAWING A complete understanding of these and other objects, features, and advantages of my invention may be gained from consideration of the following detailed description together with the accompanying drawing, in which:

FIG. 1 is a perspective view of one illustrative embodiment of my invention;

FIG. 2 is a plan view of the underside of a game wheel, showing particularly the selective positioning of the control pins for one game playable by the embodiment of FIG. 1;

FIG. 3 is a side view of the game wheel of FIG. 2;

FIG. 4 is a side view, within the machine, illustrating particularly the mechanism for the machines removal of marbles and rotation of the game wheel in the embodiment of FIG. 1;

FIG. 5 illustrates the control of the machine's actions by the selective positioning of the control pins on the game wheel, in the embodiment of FIG. 1;

FIG. 5A depicts the notched post when the control-element is secured in the notch, thereby maintaining the closure of the electrical contacts in FIG. 5; and

FIG. 6 is a partial side view showing the mechanism utilized by the player for the removal of individual marbles in the embodiment of FIG. 1 and illustrating particularly the rotation of the game wheel for each marble thus removed.

DETAILED DESCRIPTION Turning now to the drawing, the game, as seen by the player, is depicted in FIG. 1. As there seen a frame or body member 10, which may advantageously be a single molded piece of plastic, has formed on its surface an inclined rack 11 on which the marbles are placed. A game wheel 12 is also located on the surface and has successive numbers on it corresponding to the number of marbles on the rack 11. Initially when the game is started, the wheel is turned so, that the number on the wheel opposite an arrow 14 is the same as the initial number of marbles. Then, in accordance with aspects of my invention as indicated further below, the wheel turns so that the number opposite the arrow 14 remains equal to the number of marbles remaining on the rack 11.

The game is started by moving a start switch 16. A battery operated electrical circuit is then energized causing the lighting of one or the other of two windows 17 and 18. When window 17 is lit, a sign indicates Machine's Turn" When the window 18 is lit, a sign indicates Opponents Turn." I

To complete the description of the elements seen in FIG. 1, before describing the game operations themselves, there are two control levers 20 and 21. Lever 20 is pushed by the player when it is the machines turn, causing this to be indicated in window 17; lever 21 need notbe pushed by the player unless the player changes his mind immediately after he pushes lever 20 and desires to change his move. Lever 21, as discussed below, primarily serves to release the machines turn.

The machines moves are made by a hand 23 attached to a rod extending through a slot 25 in the face of the frame member 10. The opponent or player makes his move by pulling back a slide 26 which, as seen in FIG. 6, is spring tensioned. When the slide is pulled back, an individual marble is removed from the rack 11 and diverted, by stop 27, into a depression 28 in the face of the frame member and behind the rack 11. Similarly, the hand 23, when it removes a marble, causes it to fall into the depression 28.

A large depression or well 29 is advantageously provided for the storing of other game wheels identical to wheel 12 in their appearance above the frame member 10, but exercising different control for slightly different games of Nim.

In the particular game for which the wheel 12 depicted particularly in FIGS. 2 and 3 is designed, either player, i.e., the machine or the person playing the game, may take any number of marbles up to four off at one time and the player forced to take the last marble loses. Accordingly, a certain number of marbles, such as 15, are placed on the rack 11 and the player sets the wheel so that the number is opposite the arrow 14. The player now proceeds to pull backslide 26 the number of times corresponding to the number of balls or marbles he wishes to remove; as described above each time he pulls backslide 26 a marble slides down rack 11 and into depression 28. Let us assume he removes three balls. The wheel 12 will now be at position 12.

At this time the player pushes the Machine's Turn lever 20. This, as described below, closes an electrical circuit causing the arm 23 to move out from slot 25 and remove one marble only, the wheel 12 turning one position as the marble is removed. The wheel 12 is now at position 11, indicating l1 marbles left on rack 11. This is repeated with the player now removing, let us assume, two marbles; the machine will then remove three marbles. If the player then removes three marbles, the machine will remove two marbles, leaving just one. As this is the last marble, the player will have lost.

It should be pointed out that, as discussed below, after the machine's turn, whose duration is determined by the game wheel 12, the release lever 21 is automatically released and the Opponents Turn sign in window 18 is lit, indicating to the player that it is now his turn.

The intelligence of the machine is built into the game wheel 12 and the mechanisms of the game are arranged to cooperate with this built in intelligence so that the machine will always win if the player ever leaves the game in a condition other than that determined by the rule for winning at the game of Nim. This rule for a game in whichthe taker of the last marble loses and the players may take up to X marbles at each move is that when your opponent is given N(X.-l-l .-H marbles, regardless of the number of marbles he takes, if you always take the number of marbles which is the complement of (X+l) to the number of marbles he took, you must win. In the game for which the particular game wheel 12 depicted in FIGS. 2 and 3 is designed, the maximum number of marbles is set at four so that the game will, if it can, always leave the player with 5N+l marbles and, regardless of the number of marbles the player takes, will always take the complement of 5 of that number. For a different discussion of this rule, see Kasner and Newman, Mathematics and the Imagination" (Simon and Schuster, 1940), page 172.

As seen in FIGS. 2 and 3, the game wheel 12 includes a knob 30, a plurality of ratchet teeth 31, there being one tooth 3I for each marble that can be placed on the rack 11, a plurality of pins 32 and a shaft 39. In FIG. 2 there are placed, op posite each tooth 31, the number on the surface of the wheel 12; this number corresponds to the number of balls then remaining on the rack 11. As can be seen control pins 32 are located in pairs, the first pair being at positions 0 and l, the next at positions 5 and 6, next at position 10 and l l, and the last at position 15 and 16. It can be seen that the first pin corresponding to the higher number of each pair is located at the number equal to 5N+l; if the game can stop there and thereafter take the 5 s complement of the opponents move, it will win. The second control pin, at the adjacent lower number, is provided so that the machine will always take one ball if the player happens to land at the winning position. The machineis designed so that it will never make a mistake; it will always win if the player makes a mistake, but it will lose if, the player going first, the player also never makes a mistake.

It is to be pointed out that, for purposes of the exposition of my invention, certain liberties have been taken in FIG. 2. Specifically, the control pins 32 are actually not adjacent their respective numbers on the surface of the game wheel. Instead, because the control member 59, discussed below with reference to FIG. 5, is positioned ahead of the arrow 14, the control pins are similarly 90 ahead of the actual number they correspond to. Thus, if the machine is to stop its turn at the number 6, it is the control pin adjacent the number 11 in FIG. 2 which is actually controlling. Since there are four pairs of pins 32 on this wheel, they are each 90 removed from the adjacent pairs. In other embodiments, as discussed below, wherein different numbers of marbles may be removed at one time,'the pins 32 may not actually be adjacent any of the numbers conforming to the rule of the game.

To appreciate how the game wheel 12 controls the playing of the game, let us consider how the wheel 12 is moved both by the machine's turn and by the player. Turning now to FIG.

4, there is depicted the mechanism for controlling the hand 23 to remove a marble and simultaneously rotate the game wheel 12 one position. A motor 33, suitably mounted within the frame 10, and including appropriate gears, rotates a drive shaft 34 to which is attached a short crank member 35 having, in turn, an offset pivot pin 36 to which are secured a reciprocating rod 37 and a pawl lever 38. A sufficient gear ratio is provided so that the crank member 35 rotates slowly.

Reciprocating motion of rod 37 is assured by the slit 40 and stationary pin 41 secured to the frame I0. As the motor drives the crank 35, the rod moves forward and back, causing the hand 23 to emerge from the slit 25 so that the extending finger removes just one marble from the rack 11. At the same time, the pawl member 38, spring tensioned by a spring 43, is also moved forward by the crank 35. This causes a pawl hook 44 to engage one of the ratchet teeth 31 of the game wheel 12; then, upon the further ,rotation of the crank 35, the hook 44 is drawn back, pulling the game wheel tooth with it and rotating the game wheel 12 one position.

When the crank member 35 is forward, opposite to the position depicted in FIG. 4, the pawl member 38 is positioned all the way to the right and the hook 44 is slightly depressed under a guard plate 45 which prevents the hook from engaging any of the teeth 31 until it emerges from the guard plate 45 and is in proper position to engage just one tooth 31.

As long as electrical power is supplied to the motor 33, the crank 35 will rotate, causing both a removal of a marble and advancement of the game wheel 12 one position, as just described.

The pawl member 38 extends adjacent a thin metallic separator 46. To the other side of that separator 46 is positioned a similar control mechanism for the players moves, as seen in FIG. 6. As there seen the slide 26 has secured to its underside, within the frame member 10, a smaller pawl member 48 having a hooked end 49. Just as -in the case of the mechanism depicted in FIG. 4, a guard plate 52 is provided at the far end of the movement of the hook 49 to prevent premature engagement of a tooth 31 by the hook; guard plate 52 may be advantageously be integral with guard plate 45. Whereas in the case of the long ratchet member 38, the degree of motion needed to allow the hook 44 to be depressed under the guard 45, FIG. 4, was provided by the spring loading afforded by the spring 43, in the case of the mechanism of FIG. 6 this degree of motion is provided by the member 50 which secures the smaller ratchet member 48 to the slide 26. Specifically in this embodiment the member 50 is a thin spring metal element allowing the smaller pawl member 48 to pivot slightly, thereby allowing the hook 49 to be depressed under the guard plate 52.

Accordingly, when the player pulls the slide towards him, which is to the right in FIG. 6, the hook portion similarly moves, adjacent the separator 46 and under the guard plate 52. At this time as the slide 26 is moved to the right the slide is removed from the end of the rack 11 allowing one marble to be released against the stop 27 and then diverted into the depression 28, as discussed above. When the player releases the slide 26, it returns to its normal position, i.e., travels to the left in FIG. 6, due to the spring 47. As the hook 49 emerges from the end of the guard plate 52 it engages one of the game wheel teeth 31, not shown in FIG. 6, thus moving the game wheel one position.

The slide 26 is thus spring loaded, as by the spring 47 connected between the slide 26 and a post 51 attached to the frame 10. In this way for each ball of the game that the player removes, the game wheel is rotated one position so that the game wheel stays in synchronization with the number of marbles remaining on the rack l 1.

It is obvious that the player, knowing that he can take, in

. this version, any number of balls or marbles up to four, will member 59 extending towards the lever 21 and positions a small spring'6l which extends into an aperture in the lower surface of the lever 21. Also on the lever 21 are a pin 63, which extends towards the control member 59 and presses against it when the lever 21 is depressed, as discussed below, and a pin 64 extending out the end of the lever 21. This latter pin bears against the lower surface of the frame 10, not shown, as the lever 21 is spring biased upward by the spring 61.

A notched post 66 is mounted on the underside of the frame 10 and extends downward adjacent the control member 59. As seen in FIG. 5A, the post 66 has a notch 67 into which the control member 59 may be positioned, as explained subsequently. The end of the control rod 59, in accordance with an aspect of my invention, extends adjacent the control pins 32 on the game wheel 12.

In FIG. 5 the control rod 59 is depicted in its released position, as when his the players, or opponent's, turn. Thus the rod 59 is not caught by the notch 67 but is bearing against the side of the post 66. Accordingly, the end of the rod 59 is positioned considerably below the pins 32. When the rod is moved upwards, as indicated by the arrow 68, the rod is caught by the notch 67, which is the condition depicted in FIG. 5A, and the end of the rod is then positioned in the path of the pins 32.

When the player depresses the lever 20 to initiate the machines turn, contacts 69, mounted in an obvious way from the frame 10, are closed, closing the electrical circuit to the motor 33, thereby starting the operation described above with reference to FIG. 4 for the removal by the machine of a marble and simultaneous rotation of the game wheel 12. At the same time depression of the lever 20 causes the control member 59 to be moved up against the spring 61 so that the member 59 is engaged by the notch 67, and held in position. At this time the end of the control member 59 is positioned in the path of the pins 32.

As the game wheel is rotated by the motor 33, as described above, the control exercised by the control rod will not be actuated until the game wheel is moved so that one of the pins 32 engages the end of the control member 59. At that time, the pin 32 will move the end of the control member 59 just enough to dislodge it from the notch 67 in the post 66. The spring 61 will thereupon cause the control member to be pushed down, thereby rotating the lever 20 in the opposite direction to the arrow 58. This causes the contacts 69 to open, thereupon stopping the motor 33. At the same time the electrical circuit extinguishes the sign in the window 17 and instead lights the sign in the window 18, thereby advising the player that it is again his turn.

By positioning a control pin at each position determined by the rule 5N.-l-l for the game wherein a player may take up to four marbles and the player taking the last marble loses, the game wheel will always stop the removal of marbles by the machine at this winning position. A second pin 32, as discussed above, is always positioned, in this embodiment, just adjacent this first pin so that, in case the opponent stops at this position, the machine will take only one marble. Without a second pin, the machine would take up to the next winning position, which is five positions away, an illegal move in this game as only four marbles may be removed at one time.

It is obvious that other game wheels may be devised for different versions of the game of Nim. If three marbles only may be taken at a time, with the loser receiving the last marble, then the rule would be 4N+l and the pins would be effective at the positions, as indicated:

Position ..012 3 4 6 0 7 8 9 Pin ..P I

4N and the pins would be effective at the positions on the game wheel, as indicated below:

Position .0 1 11 12 Pin P P P ln consideidng the above itis to berecalled that in the ing of the game, marbles are being removed so that the position numbers are being reached in descending order. Thus the machine will always stop, because of the control mechanism described above, at the pin at the higher numbered position except when that position is the one left by the player of the game. Accordingly, in each instance the higher numbered position containing a pin complies with the rule for winning at that particular game of Nim.

In order to facilitate the change in rules, the game wheel is readily removable and replaced by a different wheel. Thus, as seen in FIG. 5, the shaft 39 of the wheel is insertable into a bar 70 extending underneath the wheel and attached at its ends to the underside of the frame 10. Advantageously, the shaft 39 may be notched and be engaged by a lightly tensioned spring member on the bar 70, without, however, interfering with the easy removal of a wheel and insertion of another.

While the electrical circuitry utilized in this embodiment of my invention has not been set forth in detail, it is believed too well known to have to depict in detail. In one specific embodiment 1 utilized circuitry driven by a pair of ordinary flashlight batteries; however, regular house voltage'may be employed if desired. The circuitry need merely be responsive to a master switch 16 to light either the window 17, if the contacts 69 are closed, or the window 18 if the contacts 69 are open. Further, when the contacts 69 are closed the motor 33 is energized.

It is to be understood that the above-described arrangements are merely illustrative of the application of the principles of my invention. Numerous other arrangements may be devised by those skilled in the art without departing from the spirit and scope of my invention.

What l claim is:

l. A game comprising means for holding a plurality of discrete articles to be removed during playing of the game,

means responsive to the player of the game for removing individual ones of said articles, I machine means for removing individual ones of said articles, and

mechanical control means for determining the number of articles removed by said machine means responsive to the number of said articles removed by said player, both said player responsive means and said machine means being physically linked to said mechanical control means.

2. A game in accordance with claim 1 wherein said control means comprises a wheel having a plurality of pins at selected positions, means for rotating said wheel responsive to said machine means for removing said articles, one of said pins determining the cessation of said machine means, and means for rotating said wheel responsive to said player means for removing said articles.

3. A game in accordance with claim 2 wherein said wheel is removable.

4. A game in accordance with claim 2 wherein said wheel includes ratchet teeth and both said rotating means include pawl means engaging said ratchet teeth.

5. A game in accordance with claim 4 further comprising guard means preventing said pawl means engaging more than one ratchet tooth at a time, both said pawl means including spring means for allowing said pawl means to be depressed under said guard means.

6. A game in accordance with claim 2 wherein said mechanical control means includes a control rod and spring means for positioning said rod in the path of said pins.

7. A game in accordance with claim 6 wherein said spring means includes a notched post for positioning said rod in the path of said pins, means for placing said rod in said notched post, and spring means biasing said rod away from said 5 notched post.

8. A game comprising means for holding a plurality of discrete articles to be removed during playing of the game,

means responsive to the player of the game for removing individual ones of said articles,

l0 machine means for removing individual ones of said articles, and mechanical control means for determining the number of articles removed by said machine means responsive to the number of said articles removed by said player.

said holding means including an inclined rack and said player responsive removing means including a slide extending across the end of said rack. 9. A game comprising means for holding a plurality of discrete articles to be removed during playing of the game, 2 means responsive to the player of the game for removing individual ones of said articles, machine means for removing individual ones of said articles, and mechanical control means for determining the number of articles removed by said machine means responsive to the number of said articles removed by said player, and

wherein said machine means for removing individual ones of said articles includes motor means, a reciprocating rod member responsive tosaid motor means, and means at the end of said rod member for displacing individual ones of said articles.

10. A game of Nim comprising a rack for holding a plurality of balls to be removed during the game,

slide means responsive to the player of the game for allow ing individual ones of said balls to be removed,

machine means for removing one of said balls during each operation,

a wheel having control elements thereon for determining the number of operations of said machine means, said wheel including means responsive to both said slide means and said machine means for rotation thereby, and

means responsive to said control elements for interrupting the operation of said machine means.

11. A game of Nim in accordance with claim 10 wherein said means responsive to both said slide means and said machine means for rotation of said wheel includes ratchet teeth,

said slide means includes first pawl means for engaging individual ones of said ratchet teeth, and

said machine means includes second pawl means for engaging individual ones of said ratchet teeth.

12. A game of Nim in accordance with claim 11 wherein said wheel is removable and said control elements are pins thereon in a discrete pattern dependent on the rules of the particular game of Nim being played.

13. A game of Nim in accordance with claim 12 wherein said machine means includes motor means, and crank means for removing individual ones of said balls from said rack.

14. A game of Nim in accordance with claim 13 wherein said means interrupting the operation of said machine means includes means for stopping said motor means, said stopping means including a control member intercepted by one of said control pins as said wheel is rotated.

15. A game comprising means for holding a plurality of articles to be removed during playing of the game,

rotatable control means having a plurality of control elements thereon positioned in accordance with the rules of the game to be played,

player means for removing said articles and rotating said control means,

machine means for removing said articles and rotating said control means, and

7 means responsive to said control elements for stopping operation of said machine means.

16. A game in accordance 'with claim wherein said stopping means includes a spring-loaded control rod and catch means for positioning the end of said rod in the path of the said control elements, said rod being released from said catch means when intercepted by one of said control elements.

17. A game in accordance with claim 16 wherein said con- 7 trol means includes ratchet teeth, said player means includes I first pawl means for engaging said teeth, and said machine means includes second pawl means for engaging said teeth. 

1. A game comprising means for holding a plurality of discrete articles to be removed during playing of the game, means responsive to the player of the game for removing individual ones of said articles, machine means for removing individual ones of said articles, and mechanical control means for determining the number of articles removed by said machine means responsive to the number of said articles removed by said player, both said player responsive means and said machine means being physically linked to said mechanical control means.
 2. A game in accordance with claim 1 wherein said control means comprises a wheel having a plurality of pins at selected positions, means for rotating said wheel responsive to said machine means for removing said articles, one of said pins determining the cessation of said machine means, and means for rotating said wheel responsive to said player means for removing said articles.
 3. A game in accordance with claim 2 wherein said wheel is removable.
 4. A game in accordance with claim 2 wherein said wheel includes ratchet teeth and both said rotating means include pawl means engaging said ratchet teeth.
 5. A game in accordance with claim 4 further comprising guard means preventing said pawl means engaging more than one ratchet tooth at a time, both said pawl means including spring means for allowing said pawl means to be depressed under said guard means.
 6. A game in accordance with claim 2 wherein said mechanical control means includes a control rod and spring means for positioning said rod in the path of said pins.
 7. A game in accordance with claim 6 wherein said spring means includes a notched post for positioning said rod in the path of said pins, means for placing said rod in said notched post, and spring means biasing said rod away from said notched post.
 8. A game comprising means for holding a plurality of discrete articles to be removed during playing of the game, means responsive to the player of the game for removing individual ones of said articles, machine means for removing individual ones of said articles, and mechanical control means for determining the number of articles removed by said machine means responsive to the number of said articles removed by said player. said holding means including an inclined rack and said player responsive removing means including a slide extending across the end of said rack.
 9. A game comprising means for holding a plurality of discrete articles to be removed during playing of the game, means responsive to the player of the game for removing individual ones of said articles, machine means for removing individual ones of said articles, and mechanical control means for determining the number of articles removed by said machine means responsive to the number of said articles removed by said player, and wherein said machine means for removing individual ones of said articles includes motor means, a reciprocating rod member responsive to said motor means, and means at the end of said rod member for displacing individual ones of saId articles.
 10. A game of Nim comprising a rack for holding a plurality of balls to be removed during the game, slide means responsive to the player of the game for allowing individual ones of said balls to be removed, machine means for removing one of said balls during each operation, a wheel having control elements thereon for determining the number of operations of said machine means, said wheel including means responsive to both said slide means and said machine means for rotation thereby, and means responsive to said control elements for interrupting the operation of said machine means.
 11. A game of Nim in accordance with claim 10 wherein said means responsive to both said slide means and said machine means for rotation of said wheel includes ratchet teeth, said slide means includes first pawl means for engaging individual ones of said ratchet teeth, and said machine means includes second pawl means for engaging individual ones of said ratchet teeth.
 12. A game of Nim in accordance with claim 11 wherein said wheel is removable and said control elements are pins thereon in a discrete pattern dependent on the rules of the particular game of Nim being played.
 13. A game of Nim in accordance with claim 12 wherein said machine means includes motor means, and crank means for removing individual ones of said balls from said rack.
 14. A game of Nim in accordance with claim 13 wherein said means interrupting the operation of said machine means includes means for stopping said motor means, said stopping means including a control member intercepted by one of said control pins as said wheel is rotated.
 15. A game comprising means for holding a plurality of articles to be removed during playing of the game, rotatable control means having a plurality of control elements thereon positioned in accordance with the rules of the game to be played, player means for removing said articles and rotating said control means, machine means for removing said articles and rotating said control means, and means responsive to said control elements for stopping operation of said machine means.
 16. A game in accordance with claim 15 wherein said stopping means includes a spring-loaded control rod and catch means for positioning the end of said rod in the path of the said control elements, said rod being released from said catch means when intercepted by one of said control elements.
 17. A game in accordance with claim 16 wherein said control means includes ratchet teeth, said player means includes first pawl means for engaging said teeth, and said machine means includes second pawl means for engaging said teeth.
 18. A game in accordance with claim 17 further comprising separator means, said first and second pawl means being adjacent opposite sides of said separator means, and guard means preventing said first and second pawl means engaging more than one of said ratchet teeth, said first and second pawl means each including spring means whereby said first and second pawl means may be depressed beneath said guard means. 